Sen. Chuck Schumer, D-N.Y., one of leaders of the effort to craft a comprehensive immigration reform bill, conceded a point Thursday often lost in the coverage over Republican divisions on the issue: Not all Democrats will likely support reform either.

According to a report in Politico on Democratic nervousness on the issue:

Sen. Chuck Schumer (D-N.Y.), one of the leaders in the group, has been candid about the fact he might not be able to get the support of the entire caucus. Instead, Schumer said he’d like to see the bill pass with broad bipartisan support.

“I’m not sure we will have every single Democrat … but we want a large number of Republicans to be able to vote for this bill because we think that will encourage the House not only to move forward but to pass a bill,” he said Thursday.

Majority Leader Harry Reid has promised that legislation will go through regular committee order and that will ultimately be key to producing a bill that gets a wide swath of support, Schumer said.

Schumer said the 2007 deal failed because of a labor-backed amendment introduced by then-Sen. Byron Dorgan (D-N.D.) that would have ended the temporary worker program after five years. Many Senate Democrats, including then-Sen. Barack Obama, supported it.

“Hopefully, such an amendment would be brought up in committee, we would see where the relative strength and weakness of that amendment is, and we’d modify the bill so it could pass,” Schumer said.

For more on the Democrat/Big Labor opposition to immigration reform see my column on how the 2007 Kennedy-McCain bill died and this column on Big Labor’s more recent efforts to negotiate a deal with the Chamber of Commerce on a guest worker program.